- Email: [email protected]
Proposal of the nano-sensing device and system using a nano-waveguide transducer for distributed sensors
Optik 121 (2010) 2117–2121
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Proposal of the nano-sensing device and system using a nano-waveguide transducer for distributed sensors P. Yabosdee a, K. Srinuanjan a, P.P. Yupapin b, a b
Department of Physics, Faculty of Science and Technology, Udornthani Rajabhat University, Udornthani, Thailand. Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
a r t i c l e in fo
abstract
Article history: Received 25 February 2009 Accepted 2 July 2009
We propose a new concept of a distributed sensing system using a nano-waveguide and an array waveguide. The small change in physical quantity affects the change in device parameters such as refractive index or length, which is relatively absorbed and observed by the resonant wavelength. In principle, the dense wavelength separation is generated by using a soliton pulse propagating within a ring resonator system, whereas a resonant signal can be stored within the nano-waveguide, i.e. a transducer, which is formed by the sensing device. Induced change in the resonant signal at each wavelength occurs, and can be detected by using the optical spectrum analyzer. Such a proposed device is suitable to perform the measurements in the nano-scale regime such as force, stress and temperature. Moreover, the distributed or multiplexed sensing applications are also available using the nanowaveguide sensing device incorporating the array waveguide, which is discussed in details. Quantum measurement using the same system is also described. & 2009 Elsevier GmbH. All rights reserved.
Keywords: Nano-sensor Distributed sensors Multiplexed sensors Nano-waveguide
1. Introduction Nano-science and technology has become the common subject that introduces many related research areas today. One of them is the nano-scale measurement resolution, i.e. nano-metrology, which can be used to support and confirm the small-scale regime of the observed physical quantities. To date, there are many techniques that can be performed using the nano-scale measurement resolutions and standards [1–4]; however, the search for new measurement standards and techniques still remains. Recently, Yupapin and Pornsuwancharoen [5] have shown the interesting result that light pulse can be stretched or compressed and stored within a tiny device known as ‘‘nano-waveguide’’. Several research works have also shown the interesting results that light can be stored within the micro-cavities [6], microsphere [7] and nano-waveguide [8]. The promising concept is that white light, i.e. continuous light spectra, can be generated, amplified and stored within a nano-waveguide, which is allowed to raise the concept of storing a narrow light pulse, i.e. a narrow spectral width. This is suitable for high-resolution measurement in terms of optical resonant wavelength, whereas the measurement resolution of pm or fm can be achieved. Many earlier works of soliton applications in either theory or experimental works are
Corresponding author.
E-mail address: [email protected] (P.P. Yupapin). 0030-4026/$ - see front matter & 2009 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2009.07.013
found in a soliton application book by Hasegawa [9]. Many of the soliton-related concepts in fiber optic are discussed by Agarwal [10]. The problems of soliton–soliton interactions [11], collision [12], rectification [13] and dispersion management [14] need to be solved and addressed. In practice, the soliton–soliton interaction would affect the dense wavelength division multiplexing (DWDM); however, this problem can be solved using the suitable free spectrum range arrangement, which can be designed [15]. To obtain the large free spectrum range, the use of optical soliton in nano-ring resonator is formed the large bandwidth signal, which can be compressed, filtered and stored within a nano-waveguide. Finally, the different resonant signals with different wavelengths are stored via the specific nano-waveguides in the array waveguide, which is available for sensing applications. The changes in physical quantities relating to the device parameters are observed and seen on the spectrum analyzer. The measurements of the related parameters with respect to the change in each wavelength can be performed in the distributed or multiplexed sensors. Quantum metrology using the present system is also described.
2. Operating principle To perform the proposed concept, a bright soliton pulse is introduced into the multi-stage nano-ring resonators as shown in Fig. 1, the input optical field (Ein) of the bright soliton pulse input
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results as shown in Eq. (3), similar to when the output field is connected and input into the other ring resonators.
3. Distributed spatial sensors
Fig. 1. A schematic of an upstream and downstream soliton generation system with a storage unit, where Rs: ring radii, ks: coupling coefficients, MRR: micro-ring resonator; NRR: nano-ring resonator.
is given by Eq. (1) [5] as T z Ein ðtÞ ¼ A sec h exp io0 t T0 2LD
ð1Þ
where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time in a frame moving at the group velocity, T= t b1 z, where b1 and b2 are the coefficients of the linear and second order terms of Taylor expansion of the propagation constant. LD = T20/|b2| is the dispersion length of the soliton pulse. T0 in equation is the initial soliton pulse width, where t is the soliton phase shift time and the frequency shift of the soliton is o0. This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity (|b2/GT20|) is given, T0 is known. For the soliton pulse in the micro-ring device, a balance should be achieved between the dispersion length (LD) and the nonlinear length (LNL = (1/GfNL)), where G = n2k0 is the length scale over which dispersive or nonlinear effects make the beam wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths; hence LD = LNL. When light propagates within the nonlinear material (medium), the refractive index (n) of light within the medium is given by n2 n ¼ n0 þn2 I ¼ n0 þ P ð2Þ Aeff where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff. For the micro-ring and nano-ring resonators, the effective mode core areas range from 0.50 to 0.1 mm2, where they found that fast light pulse can be slowed down experimentally after being input into the nano-ring. When a soliton pulse is input and propagated within a microring resonator as shown in Fig. 1, which consists of a series microring resonators, a resonant output is formed; thus, the normalized output of the light field is the ratio between the output and input fields (Eout(t) and (Ein(t)) in each round trip, which can be expressed as [5,15]
In operation, the localized soliton pulses can be stored within the micro-ring device as shown in Fig. 1. In Fig. 2, the results obtained have shown that the multi-soliton pulses can be generated and localized within the device (ring R3), where the ring radii are R1 =10 mm, R2 = 7 mm, R3 = 4 mm, where R3 = R4 (Rd = R4). The obtained results of the multi-soliton pulse generation are as follows: (a) large bandwidth signals, (b) and (c) temporal solitons, (d) localized solitons. The key advantage of the proposed system is the multi-soliton pulses, which is available for multiplex/ distributed sensing applications. A soliton communication has been recognized as a good candidate for long-distance communication. To generate a single soliton with slight difference in wavelength, the input soliton pulse is chopped (sliced) into a smaller signal spreading over the spectrum as shown in Fig. 3(b), which shows that the large bandwidth signal is generated within the first ring device. Fig. 3(c) and (d) shows the compressing in spectral width of the output signals, with the parameters used being R2 = 7 mm, R3 = R4 =R5 =5 mm. In operation, the upstream and downstream conversions of soliton generation can be performed using the system as shown in Fig. 1. Furthermore, the generated soliton/signal can be stored within a nano-waveguide (ring R4), which is confirmed by Yupapin and Poensuwancharoen [5]. The trapping pulse is circulated within the nano-waveguide (stopping/storing pulse), which can be detected, i.e. it can be slowed down and detected by any available detector. They have also found that the light pulse energy recovery can be obtained by connecting into the nano-ring device. By using Eq. (3), the output light pulse within ring R4 is obtained, where the main parameters that can provide the constant coupling energy are K31, K32 and the input power. The tunable spatial solitons can be obtained by using the array waveguide as shown in Fig. 4, which means that the multisolitons can be stored within ring R3 (or R4). The regeneration of the stored signals can be performed using ring radii R5, R6 and R7, respectively. However, the coupling losses are included within the power distribution. The induced change within ring R4 occurs and is detected related to the applied physical quantities. The sensing system is as shown in Fig. 4, whereas the signal detection device can be an optical spectrum analyzer, wavelength tuner, wavelength filter, or the recovery ring resonator.
" # pffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi Eout ðtÞ2 gÞx2 Þk pffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð1 gÞ 1 ð1 ð1 p ffiffiffiffiffiffiffiffiffiffiffi ffi 1 Þ sin 1 k þ4x 1 g k ð f =2Þ E ðtÞ ð1 x 1 g in
ð3Þ The close form of Eq. (3) indicates that a ring resonator in the particular case is very similar to a Fabry–Perot cavity, which has an input and output mirror with a field reflectivity (1 k) and a fully reflecting mirror. k is the coupling coefficient, and x= exp ( aL/2) represents a round-trip loss coefficient, f0 = kLn0 and fNL = kLn2|Ein|2 are the linear and nonlinear phase shifts, k= 2p/l is the wave propagation number in a vacuum. Here L and a are a waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the
Fig. 2. Results of the multi-soliton pulse generation, where (a) input soliton, (b) large bandwidth signals, (c) temporal soliton, (d) spatial soliton. The free spectrum range is 600 pm, and the FWHM of the pulse is 10 pm [16].
P. Yabosdee et al. / Optik 121 (2010) 2117–2121
Fig. 3. The obtained coherent pulse which is trapped within a nano-waveguide, where (a) an input soliton pulse, (b) large bandwidth signals, and (c) and (d) the compressing spectral width signals [5].
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Fig. 4. Nano-ring storage array waveguide system, (a) a sensing unit, (b) a distributed sensing system, where Ri: ring radii; ki: coupling coefficient; kij : coupling loss; ln: signal output with wavelength ln; OSA: optical spectrum analyzer.
4. Distributed quantum sensors In general, the input pulse can be a single pulse or pulse trains, where the output pulses after some round trips with random polarization are in the form as shown in Fig. 5. |HS and |VS represent the horizontal and vertical polarization components, respectively. To begin this concept, firstly, light pulse is input and chopped to form many pulses by the chaotic behavior within the micro-ring resonator. Secondly, we introduce the technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 5; polarized light can be formed and the basic vertical and horizontal polarization states corresponds to the input short and long pulses (different time), respectively. We assume those horizontally polarized pulses with a temporal separation of Dt. The coherence time of the consecutive pulses is larger than Dt. When the coupled mode is formed by the external environment, the following state is created by Eq. (4). jFSp ¼ j1; HSs j1; HSi þj2; HSs j2; HSi
ð4Þ
In the expression |k,HS, k is the number of time slots (1 or 2), where |HS and |VS denote the state of polarization in horizontal and vertical components, respectively, and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (4), for simplicity we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with
Fig. 5. A schematic diagram of polarized photon generated within a micro-ring resonator and the polarized entangled photon components.
|HS polarization shown by Eq. (4) is input into the orthogonal polarization-delay circuit shown schematically in Fig. 1. The delay circuit consists of a coupler and the difference between the roundtrip times of the micro-ring resonator, which is equal to Dt. The micro-ring tilted by changing the round trip of the ring is converted into |VS at the delay circuit output. That is the delay circuits convert jk; HS to rjk; HSþ t2 expðifÞjk þ1; VS þ rt2 expði2 fÞjk þ2; HS þ r2 t2 expði3 fÞjk þ3; VS
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where t and r are the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (4) is converted into the polarized state by the delay circuit as jFS ¼ ½j1; HSs þ expðifs Þj2; VSs ½j1; HSi þ expðifi Þj2; VSi þ½j2; HSs þ expðifs Þj3; VSs ½j2; HSi þ expðifi Þj2; VSi ¼ ½j1; HSs j1; HSi þ expðifi Þj1; HSs j2; VSi þ expðifs Þj2; VSs j1; HSi
þexp½iðfs þ fi Þj2; VSs j2; VSi þ j2; HSs j2; HSi
Fig. 6. A schematic of the entangled photon generation system; PBS: polarizing beam splitter, Ds: detectors.
þexpðifi Þj2; HSs j3; VSi þ expðifs Þj3; VSs j2; HSi þexp½iðfs þ fi Þj3; VSs j3; VSi
ð5Þ
By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the polarization entangled state as jFS ¼ j2; HSs j2; HSi þ exp½iðfs þ fi Þj2; VSs j2; VSi
ð6Þ
We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device [1–4], the strong pulses acquire an intensity-dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. The polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity, where the compensation, i.e. the measurement is performed. When polarized light propagates in the optical device, the change in birefringence is introduced. This means the change in phase of the entangled photon pair occurs. The transversal walk-off produces a shift between the ordinary and extraordinary mode, while the longitudinal walk-off introduces a time delay between horizontally and vertically polarized photons. The amount of walk-off depends on the location where the photon pairs are created within the device. This position is completely random due to the coherent nature of light in the optical device. To compensate the longitudinal timing walk-off effect, a polarization controller is recommended to ensure that the polarization rotation is the same on both photons from the entangled pair. Additionally, the compensator device is used to change the relative phase, f, of the states of the polarized light. Because of the change in birefringence, the tilting of the compensator allows one to apply a phase shift to the entangled states of the two entangled photons, which is given by Eq. (7) as [1] 1 jcS12 ¼ pffiffiffi ðjHS1 jVS2 þeif jVS1 jHS2 Þ 2
ð7Þ
In applications, the walk-off entangled state parameters involving in the measurement are related to the changes in the applied physical parameters such as force, stress, strain, heat, pressure, etc., and the optical device properties. However, the interested parameters in this proposed systems are concerned with the optical birefringence parameters, which can be given by
Df ¼
2pðnx ny ÞLw
l
ð8Þ
where Dn= (nx ny) is the optical birefringence, Lw is the entangled states walk-off length, and l is the light source wavelength. In principle, the movement of the signal and idler from the optimum location introduces the walk-off length change by the external or physical quantities, which can be compensated, i.e. measured. This effect is presented by the measurement parameter known as birefringence. The entangled photon visibility randomly
forms a pair of signal and idler, which was well described in Ref. [1]. When the chaotic signal is generated, it passes through the rotatable polarizer and polarizing beam splitter as shown in Fig. 6. The required azimuth angle is adjusted to obtain the specific orientation angle via the rotatable polarizer. The random entangled photon pair is split via a PBS and detected by the two detectors. In general, the entangled photon pairs may be formed by two different forms of the orientation angles (01, 901) or (1351, 1801), which is represented by light traveling into the optical components as described earlier. The entangled photon visibility is seen when the azimuth angle is rotated between 01 and 1801, where each peak power of the entangled photon pair is formed by each value of the maximum peak power at the specific orientation angle. Furthermore, the induced change due to the external disturbance on the stored light pulse within the sensing waveguide affects the change in the entangled photon phase shift, which is recovered by using the walk-off compensation. This is related to the change in the applied physical quantities such as force, temperature or strain on the sensing device. The proposed system is also available for the large sensing area, whereas a large number of sensing heads are required, i.e. distributed sensors.
5. Conclusion We have proposed the interesting concept where the smallscale measurement in the nano-scale resolution regime is plausible, using the nano-waveguide transducer, whereas the distributed system is also available for a large area of sensing applications. The measurement of physical quantities such as nano-force, nano-temperature, nano-strain can be performed using the proposed system. The major advantage is the sensing device can form the storing signal, which is capable of performing the long period of measurement, while the very narrow optical pulse has shown the potential of using such system for nano-scale measurement and beyond. Finally, the quantum measurement concept is also plausible, which allows one to obtain the increase in measurement resolution. By using the polarization concept, the measurement of force under zero gravity perturbation is also available.
References [1] P.P. Yupapin, Fiber optic sensing applications using the entangled state walkoff compensation, Int. Light Electron Opt. 120 (2009) 265–267. [2] P. Yabosdee, P. Phophithirankarn, P.P. Yupapin, A new concept of nano strain monitoring using strain perturbation, Int. Light Electron Opt. doi:10.1016/ j.ijleo.2008.07.032. [3] N. Pornsuwancharoen, P. Phiphithirankarn, P.P. Yupapin, J. Ali, Pulse polarization entangled photon generated by chaotic signal in a nonlinear micro ring resonator for Birefringence based sensing applications, Int. Light Electron Opt. doi:10.1016/j.optlastec.2008.12.029. [4] P.P. Yupapin, P. Yabosdee, Optimum entagled photon generated by micro ring resonator for new generation interferometry use, Int. Light Electron Opt. doi:10.1016/j.ijleo.2008.09.011.
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[5] P.P. Yupapin, N. Pornsuwancharoen, Proposed nonlinear micro ring resonator arrangement for stopping and storing light, IEEE Photon. Technol. Lett. doi:10.1109/LPT.2009.2012503. [6] M.F. Yanik, S. Fan, Stopping light all optically, Phys. Rev. Lett. 92 (2004) 083901. [7] Y. Zhao, H.W. Zhao, X.Y. Zhang, B. Yuan, S. Zhang, New mechanisms of slow light and their applications, Opt. Laser Technol. doi:10.1016/j.optlastec.2008.11.003. [8] N. Pornsuwancharoen, P.P. Yupapin, Generalized fast, slow, stop, and store light optically within a nanoring resonator, Microwave Opt. Technol. Lett. 51 (2009) 899–902. [9] A. Hasegawa (Ed.), Massive WDM and TDM Soliton Transmission Systems, Kluwer Academic Publishers, Netherland, 2000. [10] G.P. Agarwal, Nonlinear Fiber Optics, Academic Press, New York, 1995. [11] Yu.A. Simonov, Tjon, Soliton–soliton interaction in confining models, Phys. Lett. B85 (1979) 380–384.
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[12] J.K. Drohm, L.P. Kok, Yu.A. Simonov, J.A. Tjon, A.I. Veselov, Collision and rotation of solitons in three space-time dimensions, Phys. Lett. B101 (1981) 204–208. [13] T. Iizuka, Y.S. Kivshar, Optical gap solitons in nonresonant quadratic media, Phys. Rev. E 59 (1999) 7148–7151. [14] R. Ganapathy, K. Porsezian, A. Hasegawa, V.N. Serkin, Soliton interaction under soliton dispersion management, IEEE Quantum Electron. 44 (2008) 383–390. [15] P.P. Yupapin, P. Saeung, C. Li, Characteristics of complementary ring-resonator add/drop filters modeling by using graphical approach, Opt. Commun. 272 (2007) 81–86. [16] N. Sangwara, N. Pornsuwancharoen, P.P. Yupapin, Soliton pulses generation and filtering using micro ring resonators for DWDM based soliton communication, Int. J. Light Electron Opt. (2009), in press, doi:10.1016/j.ijleo. 2009.02.013.
Contents lists available at ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Proposal of the nano-sensing device and system using a nano-waveguide transducer for distributed sensors P. Yabosdee a, K. Srinuanjan a, P.P. Yupapin b, a b
Department of Physics, Faculty of Science and Technology, Udornthani Rajabhat University, Udornthani, Thailand. Advanced Research Center for Photonics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
a r t i c l e in fo
abstract
Article history: Received 25 February 2009 Accepted 2 July 2009
We propose a new concept of a distributed sensing system using a nano-waveguide and an array waveguide. The small change in physical quantity affects the change in device parameters such as refractive index or length, which is relatively absorbed and observed by the resonant wavelength. In principle, the dense wavelength separation is generated by using a soliton pulse propagating within a ring resonator system, whereas a resonant signal can be stored within the nano-waveguide, i.e. a transducer, which is formed by the sensing device. Induced change in the resonant signal at each wavelength occurs, and can be detected by using the optical spectrum analyzer. Such a proposed device is suitable to perform the measurements in the nano-scale regime such as force, stress and temperature. Moreover, the distributed or multiplexed sensing applications are also available using the nanowaveguide sensing device incorporating the array waveguide, which is discussed in details. Quantum measurement using the same system is also described. & 2009 Elsevier GmbH. All rights reserved.
Keywords: Nano-sensor Distributed sensors Multiplexed sensors Nano-waveguide
1. Introduction Nano-science and technology has become the common subject that introduces many related research areas today. One of them is the nano-scale measurement resolution, i.e. nano-metrology, which can be used to support and confirm the small-scale regime of the observed physical quantities. To date, there are many techniques that can be performed using the nano-scale measurement resolutions and standards [1–4]; however, the search for new measurement standards and techniques still remains. Recently, Yupapin and Pornsuwancharoen [5] have shown the interesting result that light pulse can be stretched or compressed and stored within a tiny device known as ‘‘nano-waveguide’’. Several research works have also shown the interesting results that light can be stored within the micro-cavities [6], microsphere [7] and nano-waveguide [8]. The promising concept is that white light, i.e. continuous light spectra, can be generated, amplified and stored within a nano-waveguide, which is allowed to raise the concept of storing a narrow light pulse, i.e. a narrow spectral width. This is suitable for high-resolution measurement in terms of optical resonant wavelength, whereas the measurement resolution of pm or fm can be achieved. Many earlier works of soliton applications in either theory or experimental works are
Corresponding author.
E-mail address: [email protected] (P.P. Yupapin). 0030-4026/$ - see front matter & 2009 Elsevier GmbH. All rights reserved. doi:10.1016/j.ijleo.2009.07.013
found in a soliton application book by Hasegawa [9]. Many of the soliton-related concepts in fiber optic are discussed by Agarwal [10]. The problems of soliton–soliton interactions [11], collision [12], rectification [13] and dispersion management [14] need to be solved and addressed. In practice, the soliton–soliton interaction would affect the dense wavelength division multiplexing (DWDM); however, this problem can be solved using the suitable free spectrum range arrangement, which can be designed [15]. To obtain the large free spectrum range, the use of optical soliton in nano-ring resonator is formed the large bandwidth signal, which can be compressed, filtered and stored within a nano-waveguide. Finally, the different resonant signals with different wavelengths are stored via the specific nano-waveguides in the array waveguide, which is available for sensing applications. The changes in physical quantities relating to the device parameters are observed and seen on the spectrum analyzer. The measurements of the related parameters with respect to the change in each wavelength can be performed in the distributed or multiplexed sensors. Quantum metrology using the present system is also described.
2. Operating principle To perform the proposed concept, a bright soliton pulse is introduced into the multi-stage nano-ring resonators as shown in Fig. 1, the input optical field (Ein) of the bright soliton pulse input
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P. Yabosdee et al. / Optik 121 (2010) 2117–2121
results as shown in Eq. (3), similar to when the output field is connected and input into the other ring resonators.
3. Distributed spatial sensors
Fig. 1. A schematic of an upstream and downstream soliton generation system with a storage unit, where Rs: ring radii, ks: coupling coefficients, MRR: micro-ring resonator; NRR: nano-ring resonator.
is given by Eq. (1) [5] as T z Ein ðtÞ ¼ A sec h exp io0 t T0 2LD
ð1Þ
where A and z are the optical field amplitude and propagation distance, respectively. T is a soliton pulse propagation time in a frame moving at the group velocity, T= t b1 z, where b1 and b2 are the coefficients of the linear and second order terms of Taylor expansion of the propagation constant. LD = T20/|b2| is the dispersion length of the soliton pulse. T0 in equation is the initial soliton pulse width, where t is the soliton phase shift time and the frequency shift of the soliton is o0. This solution describes a pulse that keeps its temporal width invariance as it propagates, and thus is called a temporal soliton. When a soliton peak intensity (|b2/GT20|) is given, T0 is known. For the soliton pulse in the micro-ring device, a balance should be achieved between the dispersion length (LD) and the nonlinear length (LNL = (1/GfNL)), where G = n2k0 is the length scale over which dispersive or nonlinear effects make the beam wider or narrower. For a soliton pulse, there is a balance between dispersion and nonlinear lengths; hence LD = LNL. When light propagates within the nonlinear material (medium), the refractive index (n) of light within the medium is given by n2 n ¼ n0 þn2 I ¼ n0 þ P ð2Þ Aeff where n0 and n2 are the linear and nonlinear refractive indexes, respectively. I and P are the optical intensity and optical power, respectively. The effective mode core area of the device is given by Aeff. For the micro-ring and nano-ring resonators, the effective mode core areas range from 0.50 to 0.1 mm2, where they found that fast light pulse can be slowed down experimentally after being input into the nano-ring. When a soliton pulse is input and propagated within a microring resonator as shown in Fig. 1, which consists of a series microring resonators, a resonant output is formed; thus, the normalized output of the light field is the ratio between the output and input fields (Eout(t) and (Ein(t)) in each round trip, which can be expressed as [5,15]
In operation, the localized soliton pulses can be stored within the micro-ring device as shown in Fig. 1. In Fig. 2, the results obtained have shown that the multi-soliton pulses can be generated and localized within the device (ring R3), where the ring radii are R1 =10 mm, R2 = 7 mm, R3 = 4 mm, where R3 = R4 (Rd = R4). The obtained results of the multi-soliton pulse generation are as follows: (a) large bandwidth signals, (b) and (c) temporal solitons, (d) localized solitons. The key advantage of the proposed system is the multi-soliton pulses, which is available for multiplex/ distributed sensing applications. A soliton communication has been recognized as a good candidate for long-distance communication. To generate a single soliton with slight difference in wavelength, the input soliton pulse is chopped (sliced) into a smaller signal spreading over the spectrum as shown in Fig. 3(b), which shows that the large bandwidth signal is generated within the first ring device. Fig. 3(c) and (d) shows the compressing in spectral width of the output signals, with the parameters used being R2 = 7 mm, R3 = R4 =R5 =5 mm. In operation, the upstream and downstream conversions of soliton generation can be performed using the system as shown in Fig. 1. Furthermore, the generated soliton/signal can be stored within a nano-waveguide (ring R4), which is confirmed by Yupapin and Poensuwancharoen [5]. The trapping pulse is circulated within the nano-waveguide (stopping/storing pulse), which can be detected, i.e. it can be slowed down and detected by any available detector. They have also found that the light pulse energy recovery can be obtained by connecting into the nano-ring device. By using Eq. (3), the output light pulse within ring R4 is obtained, where the main parameters that can provide the constant coupling energy are K31, K32 and the input power. The tunable spatial solitons can be obtained by using the array waveguide as shown in Fig. 4, which means that the multisolitons can be stored within ring R3 (or R4). The regeneration of the stored signals can be performed using ring radii R5, R6 and R7, respectively. However, the coupling losses are included within the power distribution. The induced change within ring R4 occurs and is detected related to the applied physical quantities. The sensing system is as shown in Fig. 4, whereas the signal detection device can be an optical spectrum analyzer, wavelength tuner, wavelength filter, or the recovery ring resonator.
" # pffiffiffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi Eout ðtÞ2 gÞx2 Þk pffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ¼ ð1 gÞ 1 ð1 ð1 p ffiffiffiffiffiffiffiffiffiffiffi ffi 1 Þ sin 1 k þ4x 1 g k ð f =2Þ E ðtÞ ð1 x 1 g in
ð3Þ The close form of Eq. (3) indicates that a ring resonator in the particular case is very similar to a Fabry–Perot cavity, which has an input and output mirror with a field reflectivity (1 k) and a fully reflecting mirror. k is the coupling coefficient, and x= exp ( aL/2) represents a round-trip loss coefficient, f0 = kLn0 and fNL = kLn2|Ein|2 are the linear and nonlinear phase shifts, k= 2p/l is the wave propagation number in a vacuum. Here L and a are a waveguide length and linear absorption coefficient, respectively. In this work, the iterative method is introduced to obtain the
Fig. 2. Results of the multi-soliton pulse generation, where (a) input soliton, (b) large bandwidth signals, (c) temporal soliton, (d) spatial soliton. The free spectrum range is 600 pm, and the FWHM of the pulse is 10 pm [16].
P. Yabosdee et al. / Optik 121 (2010) 2117–2121
Fig. 3. The obtained coherent pulse which is trapped within a nano-waveguide, where (a) an input soliton pulse, (b) large bandwidth signals, and (c) and (d) the compressing spectral width signals [5].
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Fig. 4. Nano-ring storage array waveguide system, (a) a sensing unit, (b) a distributed sensing system, where Ri: ring radii; ki: coupling coefficient; kij : coupling loss; ln: signal output with wavelength ln; OSA: optical spectrum analyzer.
4. Distributed quantum sensors In general, the input pulse can be a single pulse or pulse trains, where the output pulses after some round trips with random polarization are in the form as shown in Fig. 5. |HS and |VS represent the horizontal and vertical polarization components, respectively. To begin this concept, firstly, light pulse is input and chopped to form many pulses by the chaotic behavior within the micro-ring resonator. Secondly, we introduce the technique that can be used to create the entangled photon pair (qubits) as shown in Fig. 5; polarized light can be formed and the basic vertical and horizontal polarization states corresponds to the input short and long pulses (different time), respectively. We assume those horizontally polarized pulses with a temporal separation of Dt. The coherence time of the consecutive pulses is larger than Dt. When the coupled mode is formed by the external environment, the following state is created by Eq. (4). jFSp ¼ j1; HSs j1; HSi þj2; HSs j2; HSi
ð4Þ
In the expression |k,HS, k is the number of time slots (1 or 2), where |HS and |VS denote the state of polarization in horizontal and vertical components, respectively, and the subscript identifies whether the state is the signal (s) or the idler (i) state. In Eq. (4), for simplicity we have omitted an amplitude term that is common to all product states. We employ the same simplification in subsequent equations in this paper. This two-photon state with
Fig. 5. A schematic diagram of polarized photon generated within a micro-ring resonator and the polarized entangled photon components.
|HS polarization shown by Eq. (4) is input into the orthogonal polarization-delay circuit shown schematically in Fig. 1. The delay circuit consists of a coupler and the difference between the roundtrip times of the micro-ring resonator, which is equal to Dt. The micro-ring tilted by changing the round trip of the ring is converted into |VS at the delay circuit output. That is the delay circuits convert jk; HS to rjk; HSþ t2 expðifÞjk þ1; VS þ rt2 expði2 fÞjk þ2; HS þ r2 t2 expði3 fÞjk þ3; VS
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where t and r are the amplitude transmittances to cross and bar ports in a coupler. Then Eq. (4) is converted into the polarized state by the delay circuit as jFS ¼ ½j1; HSs þ expðifs Þj2; VSs ½j1; HSi þ expðifi Þj2; VSi þ½j2; HSs þ expðifs Þj3; VSs ½j2; HSi þ expðifi Þj2; VSi ¼ ½j1; HSs j1; HSi þ expðifi Þj1; HSs j2; VSi þ expðifs Þj2; VSs j1; HSi
þexp½iðfs þ fi Þj2; VSs j2; VSi þ j2; HSs j2; HSi
Fig. 6. A schematic of the entangled photon generation system; PBS: polarizing beam splitter, Ds: detectors.
þexpðifi Þj2; HSs j3; VSi þ expðifs Þj3; VSs j2; HSi þexp½iðfs þ fi Þj3; VSs j3; VSi
ð5Þ
By the coincidence counts in the second time slot, we can extract the fourth and fifth terms. As a result, we can obtain the polarization entangled state as jFS ¼ j2; HSs j2; HSi þ exp½iðfs þ fi Þj2; VSs j2; VSi
ð6Þ
We assume that the response time of the Kerr effect is much less than the cavity round-trip time. Because of the Kerr nonlinearity of the optical device [1–4], the strong pulses acquire an intensity-dependent phase shift during propagation. The interference of light pulses at a coupler introduces the output beam, which is entangled. The polarization states of light pulses are changed and converted while circulating in the delay circuit, where the polarization entangled photon pairs can be generated. The entangled photons of the nonlinear ring resonator are separated to be the signal and idler photon probability. The polarization angle adjustment device is applied to investigate the orientation and optical output intensity, where the compensation, i.e. the measurement is performed. When polarized light propagates in the optical device, the change in birefringence is introduced. This means the change in phase of the entangled photon pair occurs. The transversal walk-off produces a shift between the ordinary and extraordinary mode, while the longitudinal walk-off introduces a time delay between horizontally and vertically polarized photons. The amount of walk-off depends on the location where the photon pairs are created within the device. This position is completely random due to the coherent nature of light in the optical device. To compensate the longitudinal timing walk-off effect, a polarization controller is recommended to ensure that the polarization rotation is the same on both photons from the entangled pair. Additionally, the compensator device is used to change the relative phase, f, of the states of the polarized light. Because of the change in birefringence, the tilting of the compensator allows one to apply a phase shift to the entangled states of the two entangled photons, which is given by Eq. (7) as [1] 1 jcS12 ¼ pffiffiffi ðjHS1 jVS2 þeif jVS1 jHS2 Þ 2
ð7Þ
In applications, the walk-off entangled state parameters involving in the measurement are related to the changes in the applied physical parameters such as force, stress, strain, heat, pressure, etc., and the optical device properties. However, the interested parameters in this proposed systems are concerned with the optical birefringence parameters, which can be given by
Df ¼
2pðnx ny ÞLw
l
ð8Þ
where Dn= (nx ny) is the optical birefringence, Lw is the entangled states walk-off length, and l is the light source wavelength. In principle, the movement of the signal and idler from the optimum location introduces the walk-off length change by the external or physical quantities, which can be compensated, i.e. measured. This effect is presented by the measurement parameter known as birefringence. The entangled photon visibility randomly
forms a pair of signal and idler, which was well described in Ref. [1]. When the chaotic signal is generated, it passes through the rotatable polarizer and polarizing beam splitter as shown in Fig. 6. The required azimuth angle is adjusted to obtain the specific orientation angle via the rotatable polarizer. The random entangled photon pair is split via a PBS and detected by the two detectors. In general, the entangled photon pairs may be formed by two different forms of the orientation angles (01, 901) or (1351, 1801), which is represented by light traveling into the optical components as described earlier. The entangled photon visibility is seen when the azimuth angle is rotated between 01 and 1801, where each peak power of the entangled photon pair is formed by each value of the maximum peak power at the specific orientation angle. Furthermore, the induced change due to the external disturbance on the stored light pulse within the sensing waveguide affects the change in the entangled photon phase shift, which is recovered by using the walk-off compensation. This is related to the change in the applied physical quantities such as force, temperature or strain on the sensing device. The proposed system is also available for the large sensing area, whereas a large number of sensing heads are required, i.e. distributed sensors.
5. Conclusion We have proposed the interesting concept where the smallscale measurement in the nano-scale resolution regime is plausible, using the nano-waveguide transducer, whereas the distributed system is also available for a large area of sensing applications. The measurement of physical quantities such as nano-force, nano-temperature, nano-strain can be performed using the proposed system. The major advantage is the sensing device can form the storing signal, which is capable of performing the long period of measurement, while the very narrow optical pulse has shown the potential of using such system for nano-scale measurement and beyond. Finally, the quantum measurement concept is also plausible, which allows one to obtain the increase in measurement resolution. By using the polarization concept, the measurement of force under zero gravity perturbation is also available.
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